A Lower Bound on the Growth Constant of Polyaboloes on the Tetrakis Lattice

被引：0

作者：

Barequet, Gill ^{[1
]}

De, Minati ^{[2
]}

机构：

[1] Technion Israel Inst Technol, Dept Comp Sci, IL-3200003 Haifa, Israel

[2] Indian Inst Technol Delhi, Dept Math, New Delhi, India

来源：

COMPUTING AND COMBINATORICS, COCOON 2019 | 2019年 / 11653卷

关键词：

Lattice animals; Polyaboloes; Concatenation; Growth constant;

D O I：

10.1007/978-3-030-26176-4_2

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

A "lattice animal" is an edge-connected set of cells on a lattice. In this paper we consider the Tetrakis lattice, and provide the first lower bound on lambda(tau), the growth constant of polyaboloes (animals on this lattice), proving that lambda(tau) >= 2.4345. The proof of the bound is based on a concatenation argument and on calculus manipulations. If we also rely on an unproven assumption, which is, however, supported by empirical data, we obtain the conditional slightly-better lower bound 2.4635.

引用

页码：13 / 24

页数：12

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